I have some straight bell horns that are 26" and 29". They are powered by air compression tanks and have a very deep tone. I'm curious as to how bends in the horn would change it. Would they then need to be shorter? Will air pressure need to be increased?

1 Answer
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Very little if anything. The sound quality is affected by the bore profile (change in cross-sectional area along the tube). The amount of power needed to produce a clean output depends both on the frequency (wavelength) generated and the shape of the bell. The bell acts as an impedance-matching device to allow the physical pressure wave in the tube to disperse into free space with as little loss, diffraction, back-pressure as possible.

Some examples: a straight trumpet sounds the same (sans valves) as a modern trumpet bent into a double ellipse. Some small radios/CD players have a very long, very convoluted, internal path from driver to exit port to enhance production of low-frequency notes. This path does not significantly degrade the source waveform.

Yep. I'll just add that there is a theoretical sound difference between straight and bent horns, because the part of the sound waves (alternate cycles of compression and rarefaction) going around the outside of the curve have a longer path than the part on the inside, so the wavefront is no longer exactly in phase. But in practice, especially for low tones where the wavelength is long, this difference is completely negligible and undetectable.
– Scott WallaceFeb 14 at 14:11

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IIRC people have studied horn timbre and synthesized realistic sounding examples, and the crucial thing was that in the attack, the different partials rise at different rates. There may also be a burst of broad-spectrum noise as part of the attack. I don't know where these characteristics come from acoustically, probably from coupling between lips, mouthpiece, and air column.
– Ben CrowellFeb 14 at 22:53